Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and the for $$ \frac{x^{2}}{36}+\frac{y^{2}}{100}=1 $$

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To analyze the given ellipse equation $$ \frac{x^{2}}{36}+\frac{y^{2}}{100}=1 $$, we can identify its key features step by step.

### Step 1: Identify the center
The standard form of an ellipse is given by:
$$
\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1
$$
where $$(h, k)$$ is the center of the ellipse, $$a$$ is the semi-major axis, and $$b$$ is the semi-minor axis.

In our equation:
- $$h = 0$$
- $$k = 0$$

Thus, the center of the ellipse is at the point $$(0, 0)$$.

### Step 2: Identify $$a$$ and $$b$$
From the equation:
- $$a^{2} = 36 \Rightarrow a = \sqrt{36} = 6$$
- $$b^{2} = 100 \Rightarrow b = \sqrt{100} = 10$$

### Step 3: Identify the orientation
Since $$b > a$$, the major axis is vertical, and the minor axis is horizontal.

### Step 4: Identify the vertices
The vertices of the ellipse are located at:
- Vertices along the major axis (vertical): $$(0, k \pm b) = (0, 0 \pm 10) = (0, 10)$$ and $$(0, -10)$$
- Vertices along the minor axis (horizontal): $$(h \pm a, 0) = (0 \pm 6, 0) = (6, 0)$$ and $$(-6, 0)$$

Thus, the vertices are:
- Major axis vertices: $$(0, 10)$$ and $$(0, -10)$$
- Minor axis vertices: $$(6, 0)$$ and $$(-6, 0)$$

### Step 5: Identify the endpoints of the minor axis
The endpoints of the minor axis are the same as the vertices along the minor axis:
- Endpoints of the minor axis: $$(6, 0)$$ and $$(-6, 0)$$

### Step 6: Identify the domain and range
- **Domain**: The x-values range from $$-6$$ to $$6$$, so the domain is:
  $$
  [-6, 6]
  $$
- **Range**: The y-values range from $$-10$$ to $$10$$, so the range is:
  $$
  [-10, 10]
  $$

### Summary of the ellipse features
- **Center**: $$(0, 0)$$
- **Vertices**: Major axis: $$(0, 10)$$ and $$(0, -10)$$; Minor axis: $$(6, 0)$$ and $$(-6, 0)$$
- **Endpoints of the minor axis**: $$(6, 0)$$ and $$(-6, 0)$$
- **Domain**: $$[-6, 6]$$
- **Range**: $$[-10, 10]$$

### Graph of the ellipse
To graph the ellipse, plot the center at $$(0, 0)$$, the vertices at $$(0, 10)$$, $$(0, -10)$$, $$(6, 0)$$, and $$(-6, 0)$$, and draw the ellipse shape around these points. The ellipse will be elongated vertically due to the larger value of $$b$$.
The center of the ellipse is at $$(0, 0)$$. The vertices are $$(0, 10)$$, $$(0, -10)$$, $$(6, 0)$$, and $$(-6, 0)$$. The endpoints of the minor axis are $$(6, 0)$$ and $$(-6, 0)$$. The domain is $$[-6, 6]$$ and the range is $$[-10, 10]$$.

Find the graph of the following ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and the for \( \frac{x^{2}}{36}+\frac{y^{2}}{100}=1 \)

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